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Strong asymptotics of two-point Padé approximants for power-like multivalued functions. (English. Russian original) Zbl 1300.41009
Dokl. Math. 89, No. 2, 165-168 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 455, No. 1, 138-141 (2014).
The authors study two point Padé approximants constructed from two germs $$\omega _{0}$$ and $$\omega _{\infty }$$ of the same multivalued analytic function of the form $w\left( z\right) =w\left( z;\mathcal{A},\alpha \right) :=\prod \limits_{j=1}^{\infty }\left( z-a_{j}\right) ^{\alpha _{j}},$ where $$p\geq 2,$$ $$\alpha _{j}\in \mathbb{C}/\mathbb{Z}$$, $$\sum_{j=1}^{p}\alpha _{j}=0$$, $$\alpha _{1},\alpha _{2},\ldots,\alpha _{p}$$ are any different points in $$\mathbb{C}^{\ast }=\mathbb{C}/\left \{ 0\right \}$$, $$\mathcal{A=} \{ a_{1,}a_{2},\ldots,a_{p}\}$$, and $$\alpha =\{ \alpha _{1},\alpha _{2},\ldots,\alpha _{p}\}$$. They obtain a second order differential equation with polynomial accessory parameters and solve the equation.

##### MSC:
 41A21 Padé approximation 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)